Abstract
This paper discusses self-sustaining oscillations of
high-Reynolds-number shear layers and jets incident on edges and
corners at infinitesimal Mach number. These oscillations are
frequently sources of narrow-band sound, and are usually attributed
to the formation of discrete vortices whose interactions with the
edge or corner produce impulsive pressures that lead to the formation
of new vorticity and complete a feedback cycle of operation.
Linearized analyses of these interactions are presented in which free
shear layers are modelled by vortex sheets. Detailed results are
given for shear flows over rectangular wall apertures and shallow
cavities, and for the classical jet–edge interaction. The
operating stages of self-sustained oscillations are identified with
poles in the upper half of the complex frequency plane of a certain
impulse response function. It is argued that the real parts of these
poles determine the Strouhal numbers of the operating stages observed
experimentally for the real, nonlinear system. The response function
coincides with the Rayleigh conductivity of the ‘window’
spanned by the shear flow for wall apertures and jet–edge
interactions, and to a frequency dependent drag coefficient for
shallow wall cavities. When the interaction occurs in the
neighbourhood of an acoustic resonator, exemplified by the flue organ
pipe, the poles are augmented by a sequence of poles whose real parts
are close to the resonance frequencies of the resonator, and the
resonator can ‘speak’ at one of these frequencies (by
extracting energy from the mean flow) provided the corresponding pole
has positive imaginary part.The Strouhal numbers predicted by this theory for a shallow wall
cavity agree well with data extrapolated to zero Mach number from
measurements in air, and predictions for the jet–edge
interaction are in excellent accord with data from various sources in
the literature. In the latter case, the linear theory also agrees for
all operating stages with an empirical, nonlinear model that takes
account of the formation of discrete vortices in the jet.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
127 articles.
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